scholarly journals Analysis of boundary-domain integral equations based on a new parametrix for the mixed diffusion BVP with variable coefficient in an interior Lipschitz domain

2020 ◽  
Vol 32 (1) ◽  
pp. 59-75
Author(s):  
S. E. Mikhailov ◽  
C. F. Portillo
Keyword(s):  
Integral Equations ◽  
Lipschitz Domain ◽  
Variable Coefficient ◽  
Domain Integral

scholarly journals ANALYSIS OF DIRECT SEGREGATED BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR VARIABLE-COEFFICIENT MIXED BVPs IN EXTERIOR DOMAINS

2013 ◽  
Vol 11 (04) ◽  
pp. 1350006 ◽  
Author(s):  
O. CHKADUA ◽  
S. E. MIKHAILOV ◽  
D. NATROSHVILI
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Sobolev Spaces ◽  
Variable Coefficient ◽  
Boundary Value ◽  
Weighted Sobolev Spaces ◽  
Elliptic Partial Differential Equation ◽  
Neumann Boundary ◽  
Infinite Domains ◽  
Domain Integral

Direct segregated systems of boundary-domain integral equations are formulated for the mixed (Dirichlet–Neumann) boundary value problems for a scalar second-order divergent elliptic partial differential equation with a variable coefficient in an exterior three-dimensional domain. The boundary-domain integral equation system equivalence to the original boundary value problems and the Fredholm properties and invertibility of the corresponding boundary-domain integral operators are analyzed in weighted Sobolev spaces suitable for infinite domains. This analysis is based on the corresponding properties of the BVPs in weighted Sobolev spaces that are proved as well.

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